Binding energy of the $T_{bb}$ tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions

Abstract

We present a new determination of the $\bar b \bar b u d$ ($J^P=1^+$, $I=0$) tetraquark binding energy using lattice QCD with domain-wall light quarks and a nonperturbatively tuned three-parameter anisotropic-clover ``relativistic'' action for the $b$ quarks. We also perform a direct comparison with a reanalysis of data generated in prior work using a lattice-NRQCD action for the $b$ quarks and otherwise identical parameters. Using the new data with relativistic $b$ quarks from seven different ensembles with multiple lattice spacings and pion masses, we perform combined chiral and continuum extrapolations and obtain $(m_{T_{bb}}-m_B-m_{B^*})_{\rm RHQ}=(-76 \pm 23)$ MeV. For the NRQCD data from five ensembles, we perform chiral-only extrapolations and obtain $(m_{T_{bb}}-m_B-m_{B^*})_{\rm NRQCD}=(-74 \pm 17 \pm 10)$ MeV. The lower magnitude of the results obtained here, compared to the original analysis in Phys. Rev. D 100, 014503 (2019), is due to the use of the symmetric parts of the correlation matrices with local four-quark operators only.